If 3x + 1 = 5 , then the value of 8x3 + 1 is 2x27x3

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Using Rule 8,

3x +	1	= 5
	2x

On multiplying both sides by ( 2 / 5 )

⇒ 2x +	1	=	10
	3x		3

Cubing both sides,

∴ 8x³ +	1	+	3 × 2x ×	1	×		2x +	1		=	1000
	27x³			3x				3x			27

⇒ 8x³ +	1	+ 3 × 3 = 27
	8x³

⇒ 8x³ +	1	+ 2 ×	10	=	1000
	27x³		3		27

⇒ 8x³ +	1	=	1000	-	20
	27x³		27		3

⇒ 8x³ +	1	=	1000 - 180	=	820	= 30	10
	27x³		27		27		27

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